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I need to write a function (in Javascript) that accepts the endpoints of a line segment and an additional point and returns coordinates for the point relative to the start point. So, based on this picture:

enter image description here

function perpendicular_coords(x1,y1, x2,y2, xp,yp)

returns [xp',yp'] where xp' is the distance from (xp,yp) along a line perpendicular to the line segment, and yp' is the distance from (x1,y1) to the point where that perpendicular line intersects the line segment.

What I've tried so far:

function rotateRad(cx, cy, x, y, radians) {
    var cos = Math.cos(radians),
        sin = Math.sin(radians),
        nx = (cos * (x - cx)) + (sin * (y - cy)) + cx,
        ny = (cos * (y - cy)) - (sin * (x - cx)) + cy;
    return [nx, ny];
}

[xp', yp'] = rotateRad(x1,y1, xp, yp, Math.atan2(y2-y1,x2-x1));

I don't really understand the function; got it from https://stackoverflow.com/a/17411276/1368860

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  • $\begingroup$ What have you tried so far? If you describe what you already know how to do we'll have more chance of giving a relevant answer. For example, are you more stuck on how to solve this mathematically, or how to express it in JavaScript? $\endgroup$ – trichoplax Jan 17 '17 at 16:07
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    $\begingroup$ Oh, thanks. I'm a competent JavaScript programmer. It's the math. I'll put what I've tried in the question so it's easier to read. $\endgroup$ – Sigfried Jan 17 '17 at 16:11
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    $\begingroup$ What you're after is vector projection. Do you understand basic vector math? If not, I'm sure someone can break it down to the the basic operations. $\endgroup$ – Olivier Jan 17 '17 at 16:23
  • $\begingroup$ I don't understand vector math, but it looks like the code I'm using actually works. I think the problem I'm having is elsewhere. $\endgroup$ – Sigfried Jan 17 '17 at 22:03
  • $\begingroup$ Your $y_p$ and $x_p$ look reversed from what I would expect. Is that intentional? If not, that might be the source of whatever problems you are having. $\endgroup$ – Alan Wolfe Jan 17 '17 at 23:51
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I got a good answer on StackOverflow: https://stackoverflow.com/questions/41701713/translate-coordinates-relative-to-line-segment/41702475#41702475 from https://stackoverflow.com/users/1579780/giladd:

function perpendicular_coords(x1, y1, x2, y2, xp, yp) {
  var dx = x2 - x1,
      dy = y2 - y1;

  //find intersection point    
  var k = (dy * (xp-x1) - dx * (yp-y1)) / (dy*dy + dx*dx);
  var x4 = xp - k * dy;
  var y4 = yp + k * dx;

  var ypt = Math.sqrt((y4-y1)*(y4-y1)+(x4-x1)*(x4-x1));
  var xpt = distance(x1, y1, x2, y2, xp, yp);
  return [xpt, ypt];
}

// Distance of point from line
function distance(x1, y1, x2, y2, xp, yp) {
  var dx = x2 - x1;
  var dy = y2 - y1;

  return Math.abs(dy*xp - dx*yp + x2*y1 - y2*x1) / Math.sqrt(dy*dy + dx*dx);
}
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